Efficient minimum distance estimation with multiple rates of convergence
This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
- Phillips, P.C.B., 1989.
"Partially Identified Econometric Models,"
Cambridge University Press, vol. 5(02), pages 181-240, August.
- Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
- Kotlyarova, Yulia & Zinde-Walsh, Victoria, 2006.
"Non- and semi-parametric estimation in models with unknown smoothness,"
Elsevier, vol. 93(3), pages 379-386, December.
- Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Non And Semi-Parametric Estimation In Models With Unknown Smoothness," Departmental Working Papers 2006-15, McGill University, Department of Economics.
- Patrick GAGLIARDINI & Christian GOURIEROUX & Eric RENAULT, 2004.
"Efficient Derivative Pricing By The Extended Method of Moments,"
Swiss Finance Institute Research Paper Series
10-07, Swiss Finance Institute, revised Oct 2009.
- P. Gagliardini & C. Gourieroux & E. Renault, 2011. "Efficient Derivative Pricing by the Extended Method of Moments," Econometrica, Econometric Society, vol. 79(4), pages 1181-1232, 07.
- Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
- Douglas Staiger & James H. Stock, 1994.
"Instrumental Variables Regression with Weak Instruments,"
NBER Technical Working Papers
0151, National Bureau of Economic Research, Inc.
- Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
- Mehmet Caner, 2005.
"Nearly Singular Design In Gmm And Generalized Empirical Likelihood Estimators,"
- Caner, Mehmet, 2008. "Nearly-singular design in GMM and generalized empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 144(2), pages 511-523, June.
- Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
- Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
- Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
- Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, 07.
- Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
- Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S135-S171, 01.
- Federico M. Bandi & Peter C.B. Phillips, 2005.
"A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions,"
Cowles Foundation Discussion Papers
1522, Cowles Foundation for Research in Economics, Yale University.
- Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, vol. 137(2), pages 354-395, April.
- Peter C.B. Phillips & Joon Y. Park, 1986.
"On the Formulation of Wald Tests of Nonlinear Restrictions,"
Cowles Foundation Discussion Papers
801, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-83, September.
- Kitamura, Yuichi & Phillips, Peter C. B., 1997.
"Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments,"
Journal of Econometrics,
Elsevier, vol. 80(1), pages 85-123, September.
- Yuichi Kitamura & Peter C.B. Phillips, 1994. "Fully Modified IV, GIVE and GMM Estimation with Possibly Non-Stationary Regressions and Instruments," Cowles Foundation Discussion Papers 1082, Cowles Foundation for Research in Economics, Yale University.
- James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Lee, Lung-fei, 2010. "Pooling Estimates With Different Rates Of Convergence: A Minimum Χ2 Approach With Emphasis On A Social Interactions Model," Econometric Theory, Cambridge University Press, vol. 26(01), pages 260-299, February.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:170:y:2012:i:2:p:350-367. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.